Dynamic relationship between XRP price and correlation tensor spectra of the transaction network

ArXiv ID: 2309.05935 “View on arXiv”

Authors: Unknown

Abstract

The emergence of cryptoassets has sparked a paradigm shift in the world of finance and investment, ushering in a new era of digital assets with profound implications for the future of currency and asset management. A recent study showed that during the bubble period around the year, 2018, the price of cryptoasset, XRP has a strong anti correlation with the largest singular values of the correlation tensors obtained from the weekly XRP transaction networks. In this study, we provide a detailed analysis of the method of correlation tensor spectra for XRP transaction networks. We calculate and compare the distribution of the largest singular values of the correlation tensor using the random matrix theory with the largest singular values of the empirical correlation tensor. We investigate the correlation between the XRP price and the largest singular values for a period spanning two years. We also uncover the distinct dependence between XRP price and the singular values for bubble and non-bubble periods. The significance of time evolution of singular values is shown by comparison with the evolution of singular values of the reshuffled correlation tensor. Furthermore, we identify a set of driver nodes in the transaction networks that drives the market during the bubble period using the singular vectors.

Keywords: Correlation Tensor, Random Matrix Theory, Singular Value Decomposition (SVD), Network Analysis, Cryptoassets, Cryptoassets

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematics including correlation tensors, double Singular Value Decomposition (SVD), and random matrix theory for spectral analysis, placing it in the high math complexity range. It demonstrates empirical rigor through the analysis of real XRP transaction data over a two-year period, specific time windows, and comparison with reshuffled data, though it lacks reported backtest results or trading metrics.

  flowchart TD
    A["<b>Research Goal:</b><br>Dynamics of XRP Price vs.<br>Network Correlation Spectra"] --> B["<b>Data Input:</b><br>Weekly XRP Transaction Networks<br>(2017-2019)"]

    B --> C["<b>Methodology:</b><br>Construct Correlation Tensor<br>Perform SVD"]

    C --> D["<b>Analysis 1:</b><br>Compare Empirical Spectra<br>vs. Random Matrix Theory"]

    C --> E["<b>Analysis 2:</b><br>Identify Driver Nodes<br>via Singular Vectors"]

    D & E --> F["<b>Computational Context:</b><br>Define Bubble vs.<br>Non-Bubble Periods"]

    F --> G["<b>Key Findings/Outcomes:</b><br>1. Strong Anti-correlation during Bubble Period<br>2. Singular Values signify Market State<br>3. Driver Nodes dictate Market Dynamics"]